|n||1000||Z = 1.645|
|Construct a 90% CI|
|lower number||upper number|
|subract margin of error||add your margin of error|
A sample of 1000 items has a population standard deviation of 5.9 and a mean of 245. Construct a 90 percent confidence interval for μ.
At the end of 2016, 2017, and 2018, the average prices of a share of stock in a portfolio were $34.75, $34.65, and $31.25 respectively. To investigate the average share price at the end of 2020, a random sample of 250 stocks was drawn and their closing prices on the last trading day of 2020 were observed with a mean of 33.65 and a standard deviation of 1.85. Estimate the average price of a share of stock in the portfolio at the end of 2020 with a 95 percent confidence interval.
A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.25 and σ = 0.57. Suppose a random sample of 5000 male students is selected and the GPA for each student is calculated. Find the interval that contains 99 percent of the sample means for male students.
|P (X > 33)||0.561||???|
A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean of 32.5 lb and standard deviation of 3.25 lb, respectively, then based on a sample size of 500 boxes, what is the probability that the average weight of the boxes will exceed 33 lb?
|mean of a binomial distribution =||n * p = u|
|variance of a binomial distribution = n p ( 1 – p ) =|
If n = 52 and p = 0.66, then the standard deviation of the binomial distribution is
|P ( X > 6 customers arriving within a minute)|
|u = 4.3||6|
Consider a Poisson distribution with an average of 4.3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of more than 6 customers arriving within a minute.
An important part of the customer service responsibilities of a cable company is the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first 6 troubles reported on a given day, what is the probability that all 6will be repaired on the same day?
|z score||In the text||5-4|
|P ( X > 2.85)|
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.75 ounces and a standard deviation of 0.11 ounce. What is the probability that a randomly selected apple will contain more than 2.85 ounces?
|Z = (X-u) / Sta Dev||Solve for x|
Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 45 minutes and a standard deviation of 7 minutes. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 10 percent of the customers should receive this discount. What number of minutes do they need to wait to receive the discount?
|z score for sampling distribution|
|P ( x bar > 88)||z = ( x bar – u ) / sta dev / sq root of n|
|= (88-88.5) / 5.75|
|=standardize * SQRT(n)|
A random sample of size 350 is taken from a population with mean 88.5 and standard deviation 5.75. Find P(x bar > 88).